%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP181-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:09:35 AM UTC 2026
% Result : Unsatisfiable 2.20s 0.78s
% Output : CNFRefutation 3.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of clauses : 73 ( 73 unt; 0 nHn; 28 RR)
% Number of literals : 73 ( 72 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 89 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p12x) ).
cnf(c2,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
cnf(c3,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(inverse(X3),multiply(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
multiply(inverse(X3),multiply(X3,X2)) = multiply(multiply(inverse(X3),X3),X2),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
multiply(inverse(X2),X2) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c6,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c8,plain,
multiply(multiply(inverse(X3),X3),X2) = X2,
inference(transitivity,[status(thm)],[c6,c7]) ).
cnf(c9,plain,
multiply(inverse(X3),multiply(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c4,c8]) ).
cnf(c10,plain,
multiply(inverse(inverse(least_upper_bound(a,c))),multiply(inverse(least_upper_bound(a,c)),b)) = b,
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
b = multiply(inverse(inverse(least_upper_bound(a,c))),multiply(inverse(least_upper_bound(a,c)),b)),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,axiom,
least_upper_bound(a,c) = least_upper_bound(b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c13,plain,
inverse(least_upper_bound(a,c)) = inverse(least_upper_bound(b,c)),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,hypothesis,
inverse(least_upper_bound(X2,Y2)) = greatest_lower_bound(inverse(X2),inverse(Y2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12x_4) ).
cnf(c15,plain,
inverse(least_upper_bound(b,c)) = greatest_lower_bound(inverse(b),inverse(c)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
inverse(least_upper_bound(a,c)) = greatest_lower_bound(inverse(b),inverse(c)),
inference(transitivity,[status(thm)],[c13,c15]) ).
cnf(c17,plain,
multiply(inverse(least_upper_bound(a,c)),b) = multiply(greatest_lower_bound(inverse(b),inverse(c)),b),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
identity = multiply(inverse(X2),X2),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c19,plain,
greatest_lower_bound(identity,multiply(X3,X2)) = greatest_lower_bound(multiply(inverse(X2),X2),multiply(X3,X2)),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,axiom,
multiply(greatest_lower_bound(Y2,Z2),X2) = greatest_lower_bound(multiply(Y2,X2),multiply(Z2,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_glb2) ).
cnf(c21,plain,
multiply(greatest_lower_bound(inverse(X2),X3),X2) = greatest_lower_bound(multiply(inverse(X2),X2),multiply(X3,X2)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,plain,
greatest_lower_bound(multiply(inverse(X2),X2),multiply(X3,X2)) = multiply(greatest_lower_bound(inverse(X2),X3),X2),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,axiom,
greatest_lower_bound(X2,Y2) = greatest_lower_bound(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_glb) ).
cnf(c24,plain,
greatest_lower_bound(inverse(X2),X3) = greatest_lower_bound(X3,inverse(X2)),
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
multiply(greatest_lower_bound(inverse(X2),X3),X2) = multiply(greatest_lower_bound(X3,inverse(X2)),X2),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
greatest_lower_bound(multiply(inverse(X2),X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X3,inverse(X2)),X2),
inference(transitivity,[status(thm)],[c22,c25]) ).
cnf(c27,plain,
greatest_lower_bound(identity,multiply(X3,X2)) = multiply(greatest_lower_bound(X3,inverse(X2)),X2),
inference(transitivity,[status(thm)],[c19,c26]) ).
cnf(c28,plain,
greatest_lower_bound(X3,inverse(X2)) = greatest_lower_bound(inverse(X2),X3),
inference(substitution,[status(thm)],[c23]) ).
cnf(c29,plain,
multiply(greatest_lower_bound(X3,inverse(X2)),X2) = multiply(greatest_lower_bound(inverse(X2),X3),X2),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
greatest_lower_bound(identity,multiply(X3,X2)) = multiply(greatest_lower_bound(inverse(X2),X3),X2),
inference(transitivity,[status(thm)],[c27,c29]) ).
cnf(c31,plain,
greatest_lower_bound(identity,multiply(inverse(c),b)) = multiply(greatest_lower_bound(inverse(b),inverse(c)),b),
inference(substitution,[status(thm)],[c30]) ).
cnf(c32,plain,
multiply(greatest_lower_bound(inverse(b),inverse(c)),b) = greatest_lower_bound(identity,multiply(inverse(c),b)),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
identity = multiply(inverse(X2),X2),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c34,plain,
greatest_lower_bound(identity,multiply(inverse(X3),X2)) = greatest_lower_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,axiom,
multiply(X2,greatest_lower_bound(Y2,Z2)) = greatest_lower_bound(multiply(X2,Y2),multiply(X2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_glb1) ).
cnf(c36,plain,
multiply(inverse(X3),greatest_lower_bound(X3,X2)) = greatest_lower_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)),
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
greatest_lower_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)) = multiply(inverse(X3),greatest_lower_bound(X3,X2)),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
greatest_lower_bound(identity,multiply(inverse(X3),X2)) = multiply(inverse(X3),greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c34,c37]) ).
cnf(c39,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c23]) ).
cnf(c40,plain,
multiply(inverse(X3),greatest_lower_bound(X3,X2)) = multiply(inverse(X3),greatest_lower_bound(X2,X3)),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
greatest_lower_bound(identity,multiply(inverse(X3),X2)) = multiply(inverse(X3),greatest_lower_bound(X2,X3)),
inference(transitivity,[status(thm)],[c38,c40]) ).
cnf(c42,plain,
greatest_lower_bound(identity,multiply(inverse(c),b)) = multiply(inverse(c),greatest_lower_bound(b,c)),
inference(substitution,[status(thm)],[c41]) ).
cnf(c43,axiom,
greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c44,plain,
greatest_lower_bound(b,c) = greatest_lower_bound(a,c),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,plain,
multiply(inverse(c),greatest_lower_bound(b,c)) = multiply(inverse(c),greatest_lower_bound(a,c)),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
inverse(least_upper_bound(X2,X3)) = greatest_lower_bound(inverse(X2),inverse(X3)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c47,plain,
multiply(inverse(least_upper_bound(X2,X3)),X2) = multiply(greatest_lower_bound(inverse(X2),inverse(X3)),X2),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
greatest_lower_bound(identity,multiply(inverse(X3),X2)) = multiply(greatest_lower_bound(inverse(X2),inverse(X3)),X2),
inference(substitution,[status(thm)],[c30]) ).
cnf(c49,plain,
multiply(greatest_lower_bound(inverse(X2),inverse(X3)),X2) = greatest_lower_bound(identity,multiply(inverse(X3),X2)),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
multiply(greatest_lower_bound(inverse(X2),inverse(X3)),X2) = multiply(inverse(X3),greatest_lower_bound(X2,X3)),
inference(transitivity,[status(thm)],[c49,c41]) ).
cnf(c51,plain,
multiply(inverse(least_upper_bound(X2,X3)),X2) = multiply(inverse(X3),greatest_lower_bound(X2,X3)),
inference(transitivity,[status(thm)],[c47,c50]) ).
cnf(c52,plain,
multiply(inverse(least_upper_bound(a,c)),a) = multiply(inverse(c),greatest_lower_bound(a,c)),
inference(substitution,[status(thm)],[c51]) ).
cnf(c53,plain,
multiply(inverse(c),greatest_lower_bound(a,c)) = multiply(inverse(least_upper_bound(a,c)),a),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,plain,
multiply(inverse(c),greatest_lower_bound(b,c)) = multiply(inverse(least_upper_bound(a,c)),a),
inference(transitivity,[status(thm)],[c45,c53]) ).
cnf(c55,plain,
greatest_lower_bound(identity,multiply(inverse(c),b)) = multiply(inverse(least_upper_bound(a,c)),a),
inference(transitivity,[status(thm)],[c42,c54]) ).
cnf(c56,plain,
multiply(greatest_lower_bound(inverse(b),inverse(c)),b) = multiply(inverse(least_upper_bound(a,c)),a),
inference(transitivity,[status(thm)],[c32,c55]) ).
cnf(c57,plain,
multiply(inverse(least_upper_bound(a,c)),b) = multiply(inverse(least_upper_bound(a,c)),a),
inference(transitivity,[status(thm)],[c17,c56]) ).
cnf(c58,plain,
multiply(inverse(inverse(least_upper_bound(a,c))),multiply(inverse(least_upper_bound(a,c)),b)) = multiply(inverse(inverse(least_upper_bound(a,c))),multiply(inverse(least_upper_bound(a,c)),a)),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
X2 = multiply(inverse(X3),multiply(X3,X2)),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c60,plain,
multiply(inverse(inverse(X3)),X2) = multiply(inverse(inverse(X3)),multiply(inverse(X3),multiply(X3,X2))),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
multiply(inverse(inverse(X3)),multiply(inverse(X3),multiply(X3,X2))) = multiply(X3,X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c62,plain,
multiply(inverse(inverse(X3)),X2) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c60,c61]) ).
cnf(c63,plain,
multiply(inverse(inverse(least_upper_bound(a,c))),multiply(inverse(least_upper_bound(a,c)),a)) = multiply(least_upper_bound(a,c),multiply(inverse(least_upper_bound(a,c)),a)),
inference(substitution,[status(thm)],[c62]) ).
cnf(c64,plain,
multiply(inverse(inverse(X3)),multiply(inverse(X3),X2)) = multiply(X3,multiply(inverse(X3),X2)),
inference(substitution,[status(thm)],[c62]) ).
cnf(c65,plain,
multiply(X3,multiply(inverse(X3),X2)) = multiply(inverse(inverse(X3)),multiply(inverse(X3),X2)),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,plain,
multiply(inverse(inverse(X3)),multiply(inverse(X3),X2)) = X2,
inference(substitution,[status(thm)],[c9]) ).
cnf(c67,plain,
multiply(X3,multiply(inverse(X3),X2)) = X2,
inference(transitivity,[status(thm)],[c65,c66]) ).
cnf(c68,plain,
multiply(least_upper_bound(a,c),multiply(inverse(least_upper_bound(a,c)),a)) = a,
inference(substitution,[status(thm)],[c67]) ).
cnf(c69,plain,
multiply(inverse(inverse(least_upper_bound(a,c))),multiply(inverse(least_upper_bound(a,c)),a)) = a,
inference(transitivity,[status(thm)],[c63,c68]) ).
cnf(c70,plain,
multiply(inverse(inverse(least_upper_bound(a,c))),multiply(inverse(least_upper_bound(a,c)),b)) = a,
inference(transitivity,[status(thm)],[c58,c69]) ).
cnf(c71,plain,
b = a,
inference(transitivity,[status(thm)],[c11,c70]) ).
cnf(c72,plain,
a = b,
inference(symmetry,[status(thm)],[c71]) ).
cnf(c73,plain,
$false,
inference(resolution,[status(thm)],[c1,c72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP181-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 09:36:54 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.20/0.78 Command-line arguments: --flatten --complete-subsets
% 2.20/0.78
% 2.20/0.78 % SZS status Unsatisfiable
% 2.20/0.78
% 2.20/0.78 % SZS output start CNFRefutation
% See solution above
% 3.00/0.84
% 3.00/0.84 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------